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Distributed Omniscient Observers for Multi-Agent Systems

Ganghui Cao, Xunyuan Yin

TL;DR

The paper addresses the challenge of achieving global-state awareness in multi-agent systems using only local, relative outputs. It develops fully distributed omniscient observers for both heterogeneous and homogeneous linear MAS, exploiting block-diagonal system structure to obtain analytic observer gains and convergence guarantees while allowing inputs to remain persistently nonzero. It provides rigorous results for state estimation convergence and bounded adaptation, and demonstrates practical impact through two applications: distributed Nash equilibrium seeking and self-organized bio-inspired swarms. The work enables scalable, decentralized coordination with global situational awareness, broadening the range of tasks that MAS can reliably accomplish in engineering and swarm intelligence contexts.

Abstract

This article proposes fully distributed omniscient observers for both heterogeneous and homogeneous linear multi-agent systems, through which each agent can estimate the states of all agents. The proposed observers not only contribute to distributed Nash equilibrium seeking in multi-player games, but also provide a designable self-organization mechanism for artificial swarms to emulate biological social behaviors, including sheepdog herding and honeybee dance communication.

Distributed Omniscient Observers for Multi-Agent Systems

TL;DR

The paper addresses the challenge of achieving global-state awareness in multi-agent systems using only local, relative outputs. It develops fully distributed omniscient observers for both heterogeneous and homogeneous linear MAS, exploiting block-diagonal system structure to obtain analytic observer gains and convergence guarantees while allowing inputs to remain persistently nonzero. It provides rigorous results for state estimation convergence and bounded adaptation, and demonstrates practical impact through two applications: distributed Nash equilibrium seeking and self-organized bio-inspired swarms. The work enables scalable, decentralized coordination with global situational awareness, broadening the range of tasks that MAS can reliably accomplish in engineering and swarm intelligence contexts.

Abstract

This article proposes fully distributed omniscient observers for both heterogeneous and homogeneous linear multi-agent systems, through which each agent can estimate the states of all agents. The proposed observers not only contribute to distributed Nash equilibrium seeking in multi-player games, but also provide a designable self-organization mechanism for artificial swarms to emulate biological social behaviors, including sheepdog herding and honeybee dance communication.
Paper Structure (19 sections, 8 theorems, 40 equations, 3 figures)

This paper contains 19 sections, 8 theorems, 40 equations, 3 figures.

Table of Contents

  1. Introduction
  2. Review of the Distributed Observers Without Using Global Inputs
  3. Communication Graph
  4. Revisiting the Design Method
  5. Distributed Omniscient Observer Design
  6. Design for Heterogeneous Multi-Agent Systems
  7. Design for Homogeneous Multi-Agent Systems
  8. Further Extension
  9. Application A: Distributed Nash Equilibrium Seeking in Multi-Player Games
  10. Application B: Self-Organized Social Behavior Emergence in Artificial Swarms
  11. Confine Companions to a Convex Hull
  12. Summon Companions by Circling
  13. Simulation Results and Discussions
  14. Conclusion
  15. Appendix
  16. ...and 4 more sections

Key Result

Lemma 1

Ganghui2025arXiv Under Assumptions ubound and ooconnected, the distributed observers with node dynamics obidynamic can produce accurate state estimates for system LTIsysy, i.e., Moreover, adaptive gains $\gamma_i$ and $\gamma_{is}$ remain bounded, $\forall i \in \mathcal{N}$.

Figures (3)

  • Figure 1: Agent trajectories (start/end positions denoted by circles/crosses) in Section \ref{['CCTACH']}.
  • Figure 2: Snapshots of agent positions in Section \ref{['SCBC']}.
  • Figure 3: Agent positions vs. time in Section \ref{['SCBC']}.

Theorems & Definitions (8)

  • Lemma 1
  • Theorem 1
  • Lemma 2
  • Lemma 3
  • Theorem 2
  • Theorem 3
  • Lemma 4
  • Theorem 4